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Ketaksamaan luas segilima dan radius lingkaran luar

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Luas dari segilima konveks $ABCDE$ adalah $S$ dan panjang radius lingkaran luar $ABC, BCD, CDE, DEA, EAB$ berturut-turut adalah $R_1, R_2, R_3, R_4, R_5$. Buktikan bahwa $$R_1^4 + R_2^4 + R_3^4 + R_4^4 + R_5^4 \ge \frac{4}{5 \sin 108^{\circ}}S^2.$$


International Zhautykov Olympiad 2015, no. 6

Edited by donjar

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